FRAÇÃO | ADIÇÃO e SUBTRAÇÃO de FRAÇÕES. Método convencional e o método BORBOLETA

Summary

In this educational video, the teacher explores how to perform addition and subtraction with fractions, specifically focusing on the challenge of working with three fractions. They demonstrate the traditional method of finding the least common multiple (LCM) to equalize denominators and solve the problem. Additionally, the teacher tests the 'butterfly method' for fraction addition and subtraction, highlighting its effectiveness when applied to two fractions at a time. Through examples and simplification tips, the lesson emphasizes how both methods can achieve the same result and provides insights into where to simplify fractions for easier calculation.

Takeaways

• 😀 The MMC (Least Common Multiple) method is used to find a common denominator for adding or subtracting fractions.
• 😀 The butterfly method allows the addition and subtraction of two fractions at a time by multiplying diagonally and simplifying the result.
• 😀 When using the MMC method, the goal is to make all the denominators equal before performing the operation.
• 😀 The MMC is calculated by dividing the denominators by prime numbers to find the least common multiple.
• 😀 For the butterfly method, after multiplying the numerators and denominators diagonally, the sum or difference is calculated.
• 😀 Fractions are simplified either at the beginning or the end of the process to make the calculations easier.
• 😀 Simplifying intermediate steps (such as 52/32) is a helpful strategy to avoid larger numbers in calculations.
• 😀 The result of adding fractions using the MMC method is 25/12, which is a valid answer for addition.
• 😀 The butterfly method gives a fraction of 31/24 after applying the operation and simplifying it.
• 😀 If simplifying early, one might reach a more manageable fraction earlier, like 13/8 instead of 52/32, making the calculation easier.
• 😀 The video encourages students to engage by asking questions, leaving comments, and sharing the content with others who may need help with fraction operations.

Q & A

What is the main topic of the video?

The main topic of the video is how to add and subtract fractions, specifically exploring two methods: the MMC (Minimum Common Multiple) method and the butterfly method (borboleta).

What method is initially used to add and subtract fractions in the video?

The MMC method is used initially to add and subtract fractions. The video explains how to find a common denominator for the fractions using the Least Common Multiple (LCM) of the denominators.

How do you find the Least Common Multiple (LCM) of 2, 3, and 4?

The LCM of 2, 3, and 4 is found by dividing each number by common factors until they are all reduced to 1, then multiplying the results. The LCM is 12.

How do you make the fractions equivalent to the common denominator?

To make the fractions equivalent, each fraction is multiplied by a number that makes the denominator equal to the LCM. For example, 2 becomes 12 by multiplying both the numerator and denominator by 6.

What does the butterfly method involve?

The butterfly method involves multiplying the numerators and denominators of two fractions diagonally and then adding or subtracting the results. It is only applicable when working with two fractions at a time.

Can you use the butterfly method for three fractions at once?

No, the butterfly method cannot be applied directly to three fractions at once. However, you can apply the method to two fractions at a time, then combine the result with the third fraction using the same approach.

What happens when applying the butterfly method to the fractions 5/2 and 3/1?

When applying the butterfly method to 5/2 and 3/1, you multiply diagonally: 5 x 3 = 15 and 2 x 1 = 2. The result is 15/2.

What is the result when applying the butterfly method to 5/2, 3/1, and 3/4?

When applying the butterfly method to 5/2, 3/1, and 3/4, you first work with 5/2 and 3/1 to get 17/6, then combine that with 3/4 using the butterfly method, resulting in a final fraction of 50/24. After simplification, the final result is 25/12.

What should you do if you encounter a fraction that can be simplified during the process?

If a fraction can be simplified, it is a good idea to simplify it to make the calculations easier. Simplification can be done at any point, either during the calculation or after reaching the final result.

What are the benefits of simplifying fractions during calculations?

Simplifying fractions during calculations can make the math easier and faster. It reduces large numbers, making operations like addition, subtraction, and multiplication simpler.